Yes, in order to list to Sears you will need a Manufacturer Part Number (MPN).
To enter this value:
1. Navigate to Inventory -> inventory Management
2. Click into a product SKU using the binoculars icon
3. On the 'Details' tab, scroll down and choose the 'Attributes' section
4. Here is where you can enter your manufacturer part number in the 'Manufacturer Part #' attribute.